The best way to store cheese in the refrigerator is to wrap it in cheese paper and put it in the bottom vegetable drawer. The temperature should be between 35 and 45 degrees Fahrenheit.
Do not seal the cheese directly in plastic. Cheese needs fresh air to keep longer, and the plastic dries it out. While cheese paper is ideal, wax paper or parchment paper also work. Place the cheese in a loose plastic bag that's partially open to allow air to enter. Store it in the warmest area of the refrigerator, such as the lower vegetable drawer or on a bottom shelf farthest from the freezer unit.